What information/ remarks can I provide to help my case of ETS Leave being submitted to brigade?

Have the starting date of the academy and the start date of when the next class begins. If the next start date is way out for the next class that will strengthen your case to get the terminal leave.

I would recommend combining this with a conversation with your leadership. Make it an effort for them to understand your goals and intentions. Having a sit-down with the 1st Sgt to ask for assistance with submitting your package will achieve a few things. It will give them purpose while also checking the box that you are showing initiative. Plus the 1st Sgt can help grease the wheels with the Brass to help the request go through smoothly. Be as proactive as you can.